A purely combinatorial proof of the Hadwiger Debrunner conjecture.
Alon, N., Kleitman, D.J. (1997)
The Electronic Journal of Combinatorics [electronic only]
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Alon, N., Kleitman, D.J. (1997)
The Electronic Journal of Combinatorics [electronic only]
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P. Filliman (1990)
Discrete & computational geometry
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Discrete & computational geometry
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J. Fine (1995)
Discrete & computational geometry
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G. Panina (2003)
Open Mathematics
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All 3-dimensional convex polytopes are known to be rigid. Still their Minkowski differences (virtual polytopes) can be flexible with any finite freedom degree. We derive some sufficient rigidity conditions for virtual polytopes and present some examples of flexible ones. For example, Bricard's first and second flexible octahedra can be supplied by the structure of a virtual polytope.
Santos, Francisco, Sturmfels, Bernd (2003)
Advances in Geometry
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R.P. Stanley (1986)
Discrete & computational geometry
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Bayer, Margaret M. (2004)
The Electronic Journal of Combinatorics [electronic only]
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Branko Grünbaum, Ernest Jucovič (1974)
Czechoslovak Mathematical Journal
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G.T. Sallee (1987)
Discrete & computational geometry
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